Invariant measures for stochastic conservation laws on the line

Authors:
  • TDTheodore D. Drivas
    Theodore D. Drivas
  • ADAlexander Dunlap
    Alexander Dunlap
  • CGCole Graham
    Cole Graham
  • JLJoonhyun La
    Joonhyun La
  • LRLenya Ryzhik
    Lenya Ryzhik
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Abstract
We consider a stochastic conservation law on the line with solution-dependent diffusivity, a super-linear, sub-quadratic Hamiltonian, and smooth, spatially-homogeneous kick-type random forcing. We show that this Markov process admits a unique ergodic spatially-homogeneous invariant measure for each mean in a non-explicit unbounded set. This generalizes previous work on the stochastic Burgers equation.